Fracture often occurs in the spin forming process of thin-walled metal sheets, due to the limited fracture strain and local large plastic deformation of the sheets during the process. However, the accurate fracture prediction is a huge challenge due to the combinations of material anisotropy, complex deformation history and contact boundary conditions in the process. Though there are scattered uncoupled ductile fracture criteria proposed with various deformation mechanisms, reasons for their different fracture prediction abilities remain unclear. Thus in this study, eight popular uncoupled ductile fracture criteria i.e., Freudenthal, C-L, R-T, Brozzo, Oh, Oyane, MMC4 and DF2016, are embedded into an anisotropic constitutive model through VUMAT interface in the ABAQUS simulation software and then realized their fracture prediction in the spin forming process of an anisotropic metal sheet. The results show that the damage accumulation in the spin forming process occurs in a wide range of stress triaxiality, and the most damage accumulation occurs in the stress triaxiality range of 0–1/2. Furthermore, the eight fracture criteria have different prediction abilities in the process and a new deformation history related equivalent fracture strain is proposed to explain these differences. In addition, there exists the abnormal phenomenon that some simple damage models, as Oyane, Oh, etc. provide the more accurate fracture prediction ability than the complex and advanced MMC4 and DF2016 models in the process, and reasons for this phenomenon are explained.